Rain falls vertically into an open cart rooling along astraight horizontal track with negligible friction. As the wateraccumulates, the speed of the cart decreases. The rain stops andthe cart continues at the reduced speed. The cart springs a hole inthe bottom, and the water runs out (straight down). When the wateris completely drained, the cart speed has increased to its originalvalue.
If this is true, prove it. If false, show why it isfalse.